There is no way to manipulate Comments via Spreadsheet Services – see Issue 36756650. (Star it if you wish.)
Instead, all the “Comments” methods work on Notes.
The following method will append a new “Modified” timestamp to any existing one – not quite as nice looking as an actual Comment would be, unfortunately.
function onEdit() {
var sheet = SpreadsheetApp.getActiveSpreadsheet();
var cell = sheet.getActiveCell();
var comments = cell.getComment();
// Newline works in msgBox, but not in Note.
comments = comments + "\\nModified: " + (new Date());
//Browser.msgBox(comments);
cell.setComment(comments);
}